scholarly journals NUMERICAL MODELING OF TWO-PHASE FLOWS USING THE TWO-FLUID TWO-PRESSURE APPROACH

2004 ◽  
Vol 14 (05) ◽  
pp. 663-700 ◽  
Author(s):  
THIERRY GALLOUËT ◽  
JEAN-MARC HÉRARD ◽  
NICOLAS SEGUIN
Keyword(s):  
Volume Fraction ◽  
Local Equilibrium ◽  
Finite Volume Methods ◽  
Convective System ◽  
Two Phase Flows ◽  
Step Method ◽  
Discontinuous Solutions ◽  
Fractional Step Method ◽  
Two Phase ◽  
Two Fluid

The present paper is devoted to the computation of two-phase flows using the two-fluid approach. The overall model is hyperbolic and has no conservative form. No instantaneous local equilibrium between phases is assumed, which results in a two-velocity two-pressure model. Original closure laws for interfacial velocity and interfacial pressure are proposed. These closures allow to deal with discontinuous solutions such as shock waves and contact discontinuities without ambiguity with the definition of Rankine–Hugoniot jump relations. Each field of the convective system is investigated, providing maximum principle for the volume fraction and the positivity of densities and internal energies are ensured when focusing on the Riemann problem. Two-finite volume methods are presented, based on the Rusanov scheme and on an approximate Godunov scheme. Relaxation terms are taken into account using a fractional step method. Eventually, numerical tests illustrate the ability of both methods to compute two-phase flows.

Numerical Study of Two-Phase Flow in a Horizontal Pipeline Using an Unconditionally Hyperbolic Two-Fluid Model

2018 ◽  
Author(s):  
Raphael V. N. de Freitas ◽  
Carina N. Sondermann ◽  
Rodrigo A. C. Patricio ◽  
Aline B. Figueiredo ◽  
Gustavo C. R. Bodstein ◽  
...  
Keyword(s):  
Volume Fraction ◽  
Numerical Study ◽  
Fluid Model ◽  
Momentum Conservation ◽  
Design Stage ◽  
Two Phase Flows ◽  
Two Phase ◽  
Efficient Manner ◽  
Two Fluid Model ◽  
Two Fluid

Numerical simulation is a very useful tool for the prediction of physical quantities in two-phase flows. One important application is the study of oil-gas flows in pipelines, which is necessary for the proper selection of the equipment connected to the line during the pipeline design stage and also during the pipeline operation stage. The understanding of the phenomena present in this type of flow is more crucial under the occurrence of undesired effects in the duct, such as hydrate formation, fluid leakage, PIG passage, and valve shutdown. An efficient manner to model two-phase flows in long pipelines regarding a compromise between numerical accuracy and cost is the use of a one-dimensional two-fluid model, discretized with an appropriate numerical method. A two-fluid model consists of a system of non-linear partial differential equations that represent the mass, momentum and energy conservation principles, written for each phase. Depending on the two-fluid model employed, the system of equations may lose hyperbolicity and render the initial-boundary-value problem illposed. This paper uses an unconditionally hyperbolic two-fluid model for solving two-phase flows in pipelines in order to guarantee that the solution presents physical consistency. The mathematical model here referred to as the 5E2P (five equations and two pressures) comprises two equations of continuity and two momentum conservation equations, one for each phase, and one equation for the transport of the volume fraction. A priori this model considers two distinct pressures, one for each phase, and correlates them through a pressure relaxation procedure. This paper presents simulation cases for stratified two-phase flows in horizontal pipelines solved with the 5E2P coupled with the flux corrected transport method. The objective is to evaluate the numerical model capacity to adequately describe the velocities, pressures and volume fraction distributions along the duct.

scholarly journals Simulation of the Effect of Oil Volume Fractions in an Oil-Water Flows Along a Circular Pipe: A Finite Element Approach

2018 ◽  
Vol 10 (5) ◽  
pp. 19
Author(s):  
Ferdusee Akter ◽  
Md. Bhuyan ◽  
Ujjwal Deb
Keyword(s):  
Finite Element ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Galerkin Approximation ◽  
Computational Domain ◽  
Two Phase Flows ◽  
Two Phase ◽  
Volume Fractions ◽  
Oil In Water ◽  
Element Approach

Two phase flows in pipelines are very common in industries for the oil transportations. The aim of our work is to observe the effect of oil volume fraction in the oil in water two phase flows. The study has been accomplished using a computational model which is based on a Finite Element Method (FEM) named Galerkin approximation. The velocity profiles and volume fractions are performed by numerical simulations and we have considered the COMSOL Multiphysics Software version 4.2a for our simulation. The computational domain is 8m in length and 0.05m in radius. The results show that the velocity of the mixture decreases as the oil volume fraction increases. It should be noted that if we gradually increase the volume fractions of oil, the fluid velocity also changes and the saturated level of the volume fraction is 22.3%.

scholarly journals Two-fluid equations for two-phase flows in moving systems

2019 ◽  
Vol 51 (6) ◽  
pp. 1504-1513
Author(s):  
Byoung Jae Kim ◽  
Myung Ho Kim ◽  
Seung Wook Lee ◽  
Kyung Doo Kim
Keyword(s):  
Two Phase Flows ◽  
Two Phase ◽  
Fluid Equations ◽  
Two Fluid

Multi-Dimensional Two-Phase Flow Modeling Applied to Interior Ballistics

2011 ◽  
Vol 78 (5) ◽  
Author(s):  
Julien Nussbaum ◽  
Philippe Helluy ◽  
Jean-Marc Herard ◽  
Barbara Baschung
Keyword(s):  
Three Dimensional ◽  
Hyperbolic Model ◽  
Finite Volume Scheme ◽  
Step Method ◽  
Fractional Step Method ◽  
Two Phase ◽  
Decomposition Reactions ◽  
Solid Decomposition ◽  
The One ◽  
Complex Phenomena

Complex phenomena occur in a combustion chamber during a ballistic cycle. From the ignition of the black powder in the primer to the exit of the projectile through the muzzle, two-phase gas-powder mix undertakes various transfers in different forms. A detailed comprehension of these effects is fundamental to predict the behavior of the whole system, considering performances and safety. Although the ignition of the powder bed is three-dimensional due to the primer’s geometry, simulations generally only deal with one- or two-dimensional problem. In this study, we propose a method to simulate the two-phase flows in 1, 2 or 3 dimensions with the same system of partial differential equations. A one-pressure, conditionally hyperbolic model [1] was used and solved by a nonconservative finite volume scheme associated to a fractional step method, where each step is hyperbolic. We extend our study to a two-pressure, unconditionally hyperbolic model [2] in which a relaxation technique was applied in order to recover the one-pressure model by using the granular stress. The second goal of this study is also to propose an improved ignition model of the powder grains, by taking into account simplified chemical kinetics for decomposition reactions in the two phases. Here we consider a 0th-order solid decomposition and an unimolecular, 2nd-order gas reaction. Validation of the algorithm on several test cases is presented.

scholarly journals Computational investigation of liquid-solid slurry flow through an expansion in a rectangular duct

2014 ◽  
Vol 62 (3) ◽  
pp. 234-240 ◽  
Author(s):  
Gianandrea Vittorio Messa ◽  
Stefano Malavasi
Keyword(s):  
Volume Fraction ◽  
Particle Density ◽  
Fluid Model ◽  
Solid Volume Fraction ◽  
Solid Particles ◽  
Rectangular Duct ◽  
Two Phase ◽  
Horizontal Pipe ◽  
Two Fluid Model ◽  
Two Fluid

Abstract The flow of a mixture of liquid and solid particles at medium and high volume fraction through an expansion in a rectangular duct is considered. In order to improve the modelling of the phenomenon with respect to a previous investigation (Messa and Malavasi, 2013), use is made of a two-fluid model specifically derived for dense flows that we developed and implemented in the PHOENICS code via user-defined subroutines. Due to the lack of experimental data, the two-fluid model was validated in the horizontal pipe case, reporting good agreement with measurements from different authors for fully-suspended flows. A 3D system is simulated in order to account for the effect of side walls. A wider range of the parameters characterizing the mixture (particle size, particle density, and delivered solid volume fraction) is considered. A parametric analysis is performed to investigate the role played by the key physical mechanisms on the development of the two-phase flow for different compositions of the mixture. The main focuses are the distribution of the particles in the system and the pressure recovery

Interfacial Pressure Coefficient for Ellipsoids and Its Effect on the Two-Fluid Model Eigenvalues

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Avinash Vaidheeswaran ◽  
Martin Lopez de Bertodano
Keyword(s):  
Fluid Model ◽  
Pressure Coefficient ◽  
Well Posedness ◽  
Virtual Mass ◽  
Two Phase Flows ◽  
Two Phase ◽  
Pressure Coefficients ◽  
Interfacial Pressure ◽  
Two Fluid Model ◽  
Two Fluid

Analytical expressions for interfacial pressure coefficients are obtained based on the geometry of the bubbles occurring in two-phase flows. It is known that the shape of the bubbles affects the virtual mass and interfacial pressure coefficients, which in turn determines the cutoff void fraction for the well-posedness of two-fluid model (TFM). The coefficient used in the interfacial pressure difference correlation is derived assuming potential flow around a perfect sphere. In reality, the bubbles seen in two-phase flows get deformed, and hence, it is required to estimate the coefficients for nonspherical geometries. Oblate and prolate ellipsoids are considered, and their respective coefficients are determined. It is seen that the well-posedness limit of the TFM is determined by the combination of virtual mass and interfacial pressure coefficient used. The effect of flow separation on the coefficient values is also analyzed.

scholarly journals Wake attenuation in large Reynolds number dispersed two-phase flows

2008 ◽  
Vol 366 (1873) ◽  
pp. 2177-2190 ◽  
Author(s):  
Frédéric Risso ◽  
Véronique Roig ◽  
Zouhir Amoura ◽  
Guillaume Riboux ◽  
Anne-Marie Billet
Keyword(s):  
Reynolds Number ◽  
Volume Fraction ◽  
Bubble Diameter ◽  
Temporal Variations ◽  
The Body ◽  
Experimental Investigations ◽  
Large Reynolds Number ◽  
Two Phase Flows ◽  
Two Phase ◽  
Multi Body

The dynamics of high Reynolds number-dispersed two-phase flow strongly depends on the wakes generated behind the moving bodies that constitute the dispersed phase. The length of these wakes is considerably reduced compared with those developing behind isolated bodies. In this paper, this wake attenuation is studied from several complementary experimental investigations with the aim of determining how it depends on the body Reynolds number and the volume fraction α . It is first shown that the wakes inside a homogeneous swarm of rising bubbles decay exponentially with a characteristic length that scales as the ratio of the bubble diameter d to the drag coefficient C d , and surprisingly does not depend on α for 10 −2 ≤ α ≤10 −1 . The attenuation of the wakes in a fixed array of spheres randomly distributed in space ( α =2×10 −2 ) is observed to be stronger than that of the wake of an isolated sphere in a turbulent incident flow, but similar to that of bubbles within a homogeneous swarm. It thus appears that the wakes in dispersed two-phase flows are controlled by multi-body interactions, which cause a much faster decay than turbulent fluctuations having the same energy and integral length scale. Decomposition of velocity fluctuations into a contribution related to temporal variations and that associated to the random character of the body positions is proposed as a perspective for studying the mechanisms responsible for multi-body interactions.

A Discrete Equation Method for Two-Dimensional Calculations of Two-Phase Compressible Mixtures

2009 ◽  
Author(s):  
A. A. Leonov ◽  
V. V. Chudanov
Keyword(s):  
Volume Fraction ◽  
Hyperbolic Equations ◽  
Tangential Velocity ◽  
Accurate Estimate ◽  
Second Order ◽  
Equation Method ◽  
Discrete Equation ◽  
Riemann Solver ◽  
Discontinuous Solutions ◽  
Two Phase

At present time there are different numerical schemes to solve the hyperbolic equations system for two-phase mixture. Those schemes, mainly, rely on a second order Godunov-type scheme (Godunov, 1969), with approximate Riemann solver for the resolution of conservation equations, and set of nonconservative equations. In this paper we applied the Discrete Equation Method (DEM) processed in Saurel & Abgrall (2003) for two-phase compressible mixtures calculation using exact Riemann solver (Leonov & Chudanov, 2008). Thanks to a deeper analysis of the model, a class of schemes, those are able to converge to the correct solution even when shock waves interact with volume fraction discontinuities, was proposed. Such analysis provides a more accurate estimate of closure terms and an accurate resolution method for the conservative fluxes as well as non-conservative terms even for situations involving discontinuous solutions. The relaxation parameters are determined also, so the resulting model is free of input parameters. The second order accuracy numerical scheme was obtained using an extension of the conventional MUSCL approach. Such method allows extending for multidimensions using splitting procedures. Some common set of 2D numerical tests, calculated with previous issues of two-phase model, is produced. Here a two-phase shock tube with tangential velocity discontinuity, the advection of a square gas bubble in uniform liquid flow, the shock wave interactions with density discontinuities are presented.

Recent developments in hydrodynamic stability of two-phase flows

2012 ◽  
Vol 9 (1) ◽  
pp. 125-130
Author(s):  
A.N. Osiptsov ◽  
S.A. Boronin
Keyword(s):  
Boundary Layer ◽  
Particle Concentration ◽  
Volume Fraction ◽  
Time Interval ◽  
Dusty Gas ◽  
Two Phase Flows ◽  
Two Phase ◽  
Layer Width ◽  
Dispersed Flows ◽  
Optimal Disturbances

In the framework of two-continuum model, the stability of plane-parallel dispersed flows is analyzed. Several flow configurations are considered and several new factors are analyzed. The factors include: particle velocity slip and particle concentration non-uniformity in the main flow, non-Stokesian components of the interphase force and finite volume fraction of the dispersed phase. It is found that the new factors modify significantly the parameters of the fastest growing mode and change the critical Reynolds number of two-phase flows. A method for studying algebraic (non-modal) instability and optimal disturbances to dispersed flows is proposed. While studying the non-modal instability of the dusty-gas boundary-layer flow with a non-uniform particle concentration, we found that the disturbances with the maximum energy gain at a limited time interval are streamwise-elongated structures (streaks). As compared to the flow of a particle-free fluid, optimal disturbances to the dusty-gas flow gain much larger kinetic energy even at the boundary layer width-averaged mass concentration of ten percent, which leads to significant amplification of non-modal instability mechanism due to the presence of suspended particles.

Sign in / Sign up

Export Citation Format

Share Document